Abstract

This thesis describes new methods for extending ab initio electronic structure theory calculations to larger molecules—those requiring more than ~200 basis functions. These molecules are difficult to describe with standard methods in electronic structure theory because they require large amounts of CPU time, disk storage space, and physical memory. The work presented in this thesis develops the PS-GVB program that uses pseudospectral operator construction—a faster method of constructing two electron operators—to calculate the electronic structure of real chemical systems; and it outlines the procedure for using these operators to calculate the electronic structure of molecules with a variety of compositions, geometries, and wave functions. This thesis extends PS-GVB to metallic elements, which present particular problems for the pseudospectral method because the nature of the chemical bonding is qualitatively different between metallic elements than between non-metallic main group elements. This thesis also generalizes the Direct Inversion in the Iterative Subspace method to wave functions with arbitrary numbers of core, open-shell, and GVB natural orbitals. These wave functions are necessary to describe physical properties of chemical systems. Finally, this thesis applies these methods to study porphyrin excited states. Porphyrins appear in a variety of biological applications including the photosynthetic reaction center and the heme group, as well as applications in chemical catalysis. Semi-empirical electronic structure calculations have suggested that the porphyrin excited states are composed of coupled single excitations from the ground state. The combination of the large size of the porphyrins and the multi-configurational nature of the excited states have prevented ab initio calculations with quality basis sets on these states. Two different approaches are used: (i) Frozen Core-Four Orbital Excited States, which takes advantage of the planar geometry of many porphyrin rings to separate the σ and πorbitals of the molecules; and (ii) Self-Consistent-Four Orbital Excited States, which calculates explicitly the multi-configurational excited state energies and optimum orbitals. Both methods yield excellent agreement with experimental results suggesting that they may be used to analyze a wide variety of different porphyrin spectra.